Revisiting Bloch oscillations in homogeneous and binary chains from an exact quantum mechanical perspective

We present an exact analytic approach to study Bloch oscillations which allows to study cases where the semiclassical arguments are not valid. The method is focused on the velocity operator V. Two representative examples are addressed here: (i) the superposition of AC and DC electric fields in a one‐dimensional chain and (ii) the binary uni‐dimensional chain under the action of a static electric field. For the first case, it is demonstrated that, depending on the frequency of the AC field, an unidirectional movement emerges whose velocity depends on the magnitude of the AC and DC fields, on the phase of the AC field and on the convolution of the initial wavepacket with itself displaced by one lattice spacement. We also show the limit where the semiclassical approach can be used. For the second case, we show that the transition between two mini‐bands plays a significant role in the dynamics of the electronic wavepacket. In this case, the Bloch oscillations are characterized by two main frequencies and combinations of them.